Naming
The ham sandwich theorem takes its name from the case when n = 3 and the three objects of any shape are a chunk of ham and two chunks of bread — notionally, a sandwich — which can then all be simultaneously bisected with a single cut (i.e., a plane). In two dimensions, the theorem is known as the pancake theorem of having to cut two infinitesimally thin pancakes on a plate each in half with a single cut (i.e., a straight line).
The ham sandwich theorem is also sometimes referred to as the "ham and cheese sandwich theorem", again referring to the special case when n = 3 and the three objects are
- a chunk of ham,
- a slice of cheese, and
- two slices of bread (treated as a single disconnected object).
The theorem then states that it is possible to slice the ham and cheese sandwich in half such that each half contains the same amount of bread, cheese, and ham. It is possible to treat the two slices of bread as a single object, because the theorem only requires that the portion on each side of the plane vary continuously as the plane moves through 3-space.
The ham sandwich theorem has no relationship to the "squeeze theorem" (sometimes called the "sandwich theorem").
Read more about this topic: Ham Sandwich Theorem
Famous quotes containing the word naming:
“Husband,
who am I to reject the naming of foods
in a time of famine?”
—Anne Sexton (1928–1974)
“See, see where Christ’s blood streams in the firmament!
One drop would save my soul—half a drop! ah, my Christ!—
Ah, rend not my heart for naming of my Christ!—
Yet will I call on him!—O, spare me, Lucifer!—
Where is it now? ‘T is gone; and see where God
Stretcheth out his arm, and bends his ireful brows!—
Mountains and hills, come, come and fall on me,
And hide me from the heavy wrath of God!”
—Christopher Marlowe (1564–1593)
“The night is itself sleep
And what goes on in it, the naming of the wind,
Our notes to each other, always repeated, always the same.”
—John Ashbery (b. 1927)